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Let f(x) =sinxandg(x)=x^(3) gof(x)=...

Let f(x) `=sinxandg(x)=x^(3)`
`gof(x)=`______.

A

`sinx^(3)`

B

`sinx^(3)x`

C

`sin3x`

D

`3sinx`

Text Solution

AI Generated Solution

The correct Answer is:
To find \( g(f(x)) \), we need to follow these steps: 1. **Identify the functions**: We have \( f(x) = \sin x \) and \( g(x) = x^3 \). 2. **Substitute \( f(x) \) into \( g(x) \)**: We need to find \( g(f(x)) \), which means we will substitute \( f(x) \) into \( g(x) \). \[ g(f(x)) = g(\sin x) \] 3. **Apply the definition of \( g(x) \)**: Since \( g(x) = x^3 \), we will replace \( x \) in \( g(x) \) with \( \sin x \): \[ g(\sin x) = (\sin x)^3 \] 4. **Write the final answer**: Therefore, we can conclude that: \[ g(f(x)) = \sin^3 x \] Thus, the final answer is: \[ g(f(x)) = \sin^3 x \] ---
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